Finite Group Databasebeta

← #11675221

Subgroups — #11675221

Order 768.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85830C211yesmaximal, characteristic, complemented
2#85828C211yesmaximal, characteristic, complemented
3C3×C4×#135C211yesmaximal, characteristic
4#83902C212yesmaximal
5#82533C211yesmaximal, characteristic, complemented
6#82508C211yesmaximal, characteristic, complemented
7#79702C212yesmaximal, complemented
8#79699C212yesmaximal, complemented
9#79628C212yesmaximal, complemented
10#79626C212yesmaximal, complemented
11#79623C212yesmaximal, complemented
12#79619C212yesmaximal, complemented
13#79571C212yesmaximal, complemented
14#79568C212yesmaximal, complemented
15#79198C212yesmaximal, complemented
16#78828C212yesmaximal, complemented
17#78821C212yesmaximal, complemented
18C2×#4681C211yesmaximal, characteristic, complemented
19#78445C211yesmaximal, characteristic, complemented
20#61330—31nomaximal, Sylow
21C2×C3×#135C2211yescharacteristic
22C3×C4×#41C2211yescharacteristic
23C3×C4×#41C2211yescharacteristic
24#5827C2212yes—
25#5825C2212yes—
26C2×#951C2212yes—
27#5570C2212yes—
28#5567C2212yes—
29#5567C2212yes—
30Q8×Dic6C2212yes—
31#5543—22no—
32#5543C2212yes—
33#5542C2212yes—
34#5542C2212yes—
35#5541—22no—
36#5541—22no—
37D4×Dic6—22no—
38D4×Dic6C2212yes—
39#5519—22no—
40#5519C2212yes—
41#5518—22no—
42#5516C2212yes—
43#5470—21no—
44#5470—21no—
45#5470—21no—
46#5470C2211yescharacteristic
47C2×#869—21no—
48C2×#869C2211yescharacteristic
49C2×#869C2211yescharacteristic
50C3×C4×Q16C2211yescharacteristic
51C3×C4×Q16C2211yescharacteristic
52C3×C4×SD16C2211yescharacteristic
53C3×C4×SD16C2211yescharacteristic
54C3×C4×SD16C2211yescharacteristic
55C3×C4×SD16C2211yescharacteristic
56C3×C4×D8C2211yescharacteristic
57C3×C4×D8C2211yescharacteristic
58C3×#427C2211yescharacteristic
59C3×#416C2211yescharacteristic
60C3×#416C2211yescharacteristic
61C2×C3×C4×C8C2211yescharacteristic
62#5232C2212yes—
63#5182C2214yes—
64#5166C2214yes—
65#5162C2214yes—
66#5153C2214yes—
67C2×#816C2212yes—
68C2×#816C2212yes—
69#5102C2212yes—
70#5101C2212yes—
71#5031C2212yes—
72#5031C2212yes—
73#5021C2212yes—
74#5020C2212yes—
75#5019C2212yes—
76#5019C2212yes—
77#5008C2212yes—
78#5007C2212yes—
79#5004C2212yes—
80#4995C2212yes—
81#4924C2211yescharacteristic
82#4877C2214yes—
83#4875C2214yes—
84#4857C2214yes—
85#4854C2214yes—
86#4797C2214yes—
87#4792C2214yes—
88#4790C2214yes—
89#4789C2214yes—
90#4768C2214yes—
91#4765C2214yes—
92#4758C2214yes—
93#4757C2214yes—
94#4681C2212yes—
95#4681C2212yes—
96#4681C2212yes—
97#4681C2212yes—
98#4679C2212yes—
99#4679C2212yes—
100C8×Dic6C2212yes—
101C8×Dic6C2212yes—
102#3509—31no—
103#3503—31no—
104#3374—32no—
105#3372—32no—
106#3369—32no—
107#3367—32no—
108#3364—32no—
109#3363—32no—
110#3360—32no—
111#3359—32no—
112#3137—32no—
113C2×#487—31no—
114#3082—32no—
115#3079—31no—
116#3046—32no—
117#3039—31no—
118#2960—31no—
119#2947—32no—
120C4×#135D311yescharacteristic
121C2×C3×#41C2311yescharacteristic
122C2×C3×#41C2311yescharacteristic
123C22×Dic6—21no—
124C22×Dic6—22no—
125C22×Dic6C2312yes—
126C3×#135—24no—
127C2×C3×Q16C2311yescharacteristic
128C2×C3×SD16C2311yescharacteristic
129C2×C3×SD16C2311yescharacteristic
130C2×C3×D8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C22×C3×C8C2311yescharacteristic
133C3×C4×Q8C2311yescharacteristic
134C3×C4×Q8C2311yescharacteristic
135C3×C4×Q8C2311yescharacteristic
136C3×C4×Q8C2311yescharacteristic
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4C2311yescharacteristic
142C3×C4×D4C2311yescharacteristic
143C3×C4×D4C2311yescharacteristic
144C3×C4×D4C2311yescharacteristic
145C3×#117—21no—
146C3×#117—21no—
147C3×#117C2311yescharacteristic
148C3×#117C2311yescharacteristic
149C2×C3×C42—21no—
150C2×C3×C42—21no—
151C2×C3×C42C2311yescharacteristic
152#951—28no—
153Q8×Dic3C2314yes—
154#944C2314yes—
155C2×#216C2314yes—
156#936C2314yes—
157#935—24no—
158D4×Dic3—24no—
159D4×Dic3C2314yes—
160C2×#214C2314yes—
161#926—22no—
162#926—22no—
163#926—22no—
164#926C2312yes—
165C2×C4⋊Dic3—21no—
166C2×C4⋊Dic3—21no—
167C2×C4⋊Dic3—21no—
168C2×C4⋊Dic3—22no—
169C2×C4⋊Dic3—22no—
170C2×C4⋊Dic3C2312yes—
171#924—22no—
172#924—22no—
173#924—22no—
174#924—22no—
175#924—22no—
176#924—22no—
177#924D412yes—
178#924D412yes—
179C2×#208C2312yes—
180#890—24no—
181#890C2314yes—
182#889—24no—
183#889—24no—
184#888—24no—
185#888C2314yes—
186#887C2314yes—
187#887C2314yes—
188#879—24no—
189#879—24no—
190#878—24no—
191#878—24no—
192#878—24no—
193#877—24no—
194#870—22no—
195#870—22no—
196#870—22no—
197#870D412yes—
198#869—22no—
199#869—21no—
200#869—21no—
201#869—21no—
202#869—21no—
203#869—22no—
204#869—22no—
205#869D411yescharacteristic
206#869D411yescharacteristic
207#869C2312yes—
208#869C2312yes—
209#869C2312yes—
210#869C2312yes—
211C4×Dic6—22no—
212C4×Dic6—22no—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C4×Dic6C2312yes—
218C4×Dic6C2312yes—
219C3×#107C2311yescharacteristic
220C3×#107C2311yescharacteristic
221C3×#106C2311yescharacteristic
222C3×#106C2311yescharacteristic
223C3×#103C2311yescharacteristic
224C3×#103C2311yescharacteristic
225C3×#103C2311yescharacteristic
226C3×#103C2311yescharacteristic
227C3×#102C2311yescharacteristic
228C3×#102C2311yescharacteristic
229C3×#102C2311yescharacteristic
230C3×#102C2311yescharacteristic
231C3×C4×C8C2311yescharacteristic
232C3×C4×C8C2311yescharacteristic
233C3×C4×C8C2311yescharacteristic
234C3×C4×C8C2311yescharacteristic
235#835C2314yes—
236#832C2314yes—
237#816C2314yes—
238#816C2314yes—
239#816C2314yes—
240#816C2314yes—
241#815C2314yes—
242Dic3⋊C8C2314yes—
243Dic3⋊C8C2314yes—
244C8×Dic3C2314yes—
245#810C2314yes—
246#810C2314yes—
247#808C2314yes—
248#807C2314yes—
249C4⋊(C3⋊C8)C2312yes—
250C4⋊(C3⋊C8)C2312yes—
251C2×#137—32no—
252C2×#135C2×D311yescharacteristic
253Q82—32no—
254#557—32no—
255#557—32no—
256#557—32no—
257#556—32no—
258#556—32no—
259#554—32no—
260#554—62no—
261#552—62no—
262#552—62no—
263D4×Q8—32no—
264D4×Q8—62no—
265#544—32no—
266#544—62no—
267#541—62no—
268#536—32no—
269#533—31no—
270#533—61no—
271#533—61no—
272#533—61no—
273C2×C4⋊Q8—31no—
274C2×C4⋊Q8—31no—
275C2×C4⋊Q8—61no—
276#520—32no—
277#519—32no—
278C4×#41C2×D311yescharacteristic
279C4×#41C2×D311yescharacteristic
280#491—34no—
281#489—34no—
282#488—34no—
283#487—34no—
284#487—32no—
285#487—32no—
286#487—32no—
287#487—32no—
288#479—34no—
289#479—34no—
290#477—32no—
291#477—34no—
292#476—32no—
293#475—32no—
294#475—34no—
295#474—32no—
296#464—34no—
297#463—34no—
298#462—34no—
299#462—32no—
300#462—32no—
301#461—34no—
302#461—32no—
303#461—32no—
304#446—32no—
305#446—32no—
306C8×Q8—32no—
307C8×Q8—32no—
308#441—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16C2×D311yescharacteristic
312C4×Q16C2×D311yescharacteristic
313C4×SD16—34no—
314C4×SD16C2×D311yescharacteristic
315C4×SD16C2×D311yescharacteristic
316C4×SD16C2×D311yescharacteristic
317C4×SD16C2×D311yescharacteristic
318C4×D8C2×D311yescharacteristic
319C4×D8C2×D311yescharacteristic
320#428—32no—
321#427C2×D311yescharacteristic
322#424—32no—
323#423—31no—
324#419—32no—
325#417—32no—
326#416C2×D311yescharacteristic
327#416C2×D311yescharacteristic
328C2×#103—32no—
329C2×#103—32no—
330#405—32no—
331C2×C4×C8C2×D311yescharacteristic
332C3×#41—22no—
333C3×#41—22no—
334C3×#41—22no—
335C3×#41#4114yes—
336C2×C3×Q8C2411yescharacteristic
337C2×C3×Q8C2411yescharacteristic
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4C2411yescharacteristic
341C2×C3×D4C2411yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4C2×D411yescharacteristic
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2411yescharacteristic
351C22×Dic3—22no—
352C22×Dic3—22no—
353C22×Dic3—24no—
354C2×Dic6—24no—
355C2×Dic6—24no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—84no—
361C2×Dic6—82no—
362C2×Dic6C2×D412yes—
363C2×Dic6C2×D412yes—
364C2×Dic6C2414yes—
365C3×Q16—22no—
366C3×SD16—22no—
367C3×SD16—22no—
368C3×D8—22no—
369C2×C3×C8—22no—
370C2×C3×C8—22no—
371C2×C3×C8C2411yescharacteristic
372C2×C3×C8C2411yescharacteristic
373C2×C3×C8C2411yescharacteristic
374C2×C3×C8C2411yescharacteristic
375C3×C4⋊C4—21no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4C2411yescharacteristic
380C3×C4⋊C4C2411yescharacteristic
381C3×C4⋊C4C2411yescharacteristic
382C3×C4⋊C4C2411yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—21no—
392C3×C42—21no—
393C3×C42—21no—
394C3×C42—21no—
395C3×C42C2×D411yescharacteristic
396C3×C42C2×D411yescharacteristic
397C3×C42C2411yescharacteristic
398C3×C42C2411yescharacteristic
399#217—24no—
400#217—24no—
401#217—24no—
402#217C2×D414yes—
403#216—28no—
404#214—28no—
405C4⋊Dic3—22no—
406C4⋊Dic3—22no—
407C4⋊Dic3—22no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3—24no—
413C4⋊Dic3—24no—
414C4⋊Dic3C2×D412yes—
415C4⋊Dic3C2×D412yes—
416C4⋊Dic3C2×D412yes—
417C4⋊Dic3C2×D412yes—
418C4⋊Dic3C2414yes—
419Dic3⋊C4—24no—
420Dic3⋊C4—24no—
421Dic3⋊C4—24no—
422Dic3⋊C4—24no—
423Dic3⋊C4—24no—
424Dic3⋊C4—24no—
425Dic3⋊C4C2×D414yes—
426Dic3⋊C4C2×D414yes—
427C4×Dic3—24no—
428C4×Dic3—24no—
429C4×Dic3—24no—
430C4×Dic3C2414yes—
431#208—24no—
432C2×C3⋊C8C2414yes—
433C2×#41C22×D311yescharacteristic
434C2×#41C22×D311yescharacteristic
435C22×Q8—32no—
436C22×Q8—62no—
437C22×Q8—61no—
438#137—68no—
439#135—24no—
440C2×Q16—34no—
441C2×Q16C22×D311yescharacteristic
442C2×SD16—34no—
443C2×SD16C22×D311yescharacteristic
444C2×SD16C22×D311yescharacteristic
445C2×D8C22×D311yescharacteristic
446C2×M16—32no—
447C22×C8C22×D311yescharacteristic
448C22×C8C22×D311yescharacteristic
449C4⋊Q8—34no—
450C4⋊Q8—34no—
451C4⋊Q8—31no—
452C4⋊Q8—31no—
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—32no—
456C4⋊Q8—32no—
457C4⋊Q8—62no—
458C4⋊Q8—62no—
459C4⋊Q8—62no—
460C4⋊Q8—64no—
461C4⋊Q8—61no—
462C4⋊Q8—61no—
463C4⋊Q8—61no—
464C4⋊Q8—61no—
465#126—64no—
466#126—64no—
467#125—34no—
468#125—32no—
469#125—62no—
470#125—62no—
471#125—62no—
472#125—64no—
473#125—64no—
474#125—64no—
475#124—34no—
476#123—64no—
477C22⋊Q8—32no—
478C22⋊Q8—32no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—64no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C4×Q8—32no—
489C4×Q8—32no—
490C4×Q8—34no—
491C4×Q8—34no—
492C4×Q8—34no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—62no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8C22×D311yescharacteristic
500C4×Q8C22×D311yescharacteristic
501C4×Q8C22×D311yescharacteristic
502C4×Q8C22×D311yescharacteristic
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—34no—
508C4×D4—64no—
509C4×D4C22×D311yescharacteristic
510C4×D4C22×D311yescharacteristic
511C4×D4C22×D311yescharacteristic
512C4×D4C22×D311yescharacteristic
513#117—21no—
514#117—21no—
515#117—32no—
516#117—64no—
517#117—62no—
518#117—62no—
519#117—62no—
520#117C22×D311yescharacteristic
521#117C22×D311yescharacteristic
522C2×C4⋊C4—32no—
523C2×C4⋊C4—62no—
524C2×C4⋊C4—62no—
525C2×C4⋊C4—61no—
526C2×C4⋊C4—61no—
527C2×C4⋊C4—61no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42C22×D311yescharacteristic
531#107—34no—
532#107C22×D311yescharacteristic
533#107C22×D311yescharacteristic
534#106—34no—
535#106C22×D311yescharacteristic
536#106C22×D311yescharacteristic
537C4⋊C8—34no—
538C4⋊C8—34no—
539C4⋊C8—32no—
540C4⋊C8—32no—
541#103—34no—
542#103—34no—
543#103—34no—
544#103—34no—
545#103—34no—
546#103—34no—
547#103—34no—
548#103C22×D311yescharacteristic
549#103C22×D311yescharacteristic
550#103C22×D311yescharacteristic
551#103C22×D311yescharacteristic
552#102—34no—
553#102C22×D311yescharacteristic
554#102C22×D311yescharacteristic
555#102C22×D311yescharacteristic
556#102C22×D311yescharacteristic
557#97—34no—
558C4×C8—34no—
559C4×C8C22×D311yescharacteristic
560C4×C8C22×D311yescharacteristic
561C4×C8C22×D311yescharacteristic
562C4×C8C22×D311yescharacteristic
563C23×C3—21no—
564C23×C3—21no—
565C23×C3C22×D411yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8C2×#4112yes—
570C3×D4—24no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—42no—
575C3×D4C2×#4112yes—
576C2×C3×C4—21no—
577C2×C3×C4—24no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C22×D411yescharacteristic
595C2×C3×C4C2×#4112yes—
596C2×C3×C42−1+412yes—
597C2×C3×C4C2511yescharacteristic
598C2×Dic3—24no—
599C2×Dic3—24no—
600C2×Dic3—44no—
601C2×Dic3—84no—
602C2×Dic3—82no—
603C2×Dic3C22×D414yes—
604C2×Dic3C22×D414yes—
605Dic6—24no—
606Dic6—24no—
607Dic6—24no—
608Dic6—24no—
609Dic6—44no—
610Dic6—44no—
611Dic6—84no—
612Dic6—82no—
613C3×C8—21no—
614C3×C8—21no—
615C3×C8—21no—
616C3×C8—21no—
617C3⋊C8—24no—
618#41—22no—
619#41—22no—
620#41—22no—
621#41#23514yes—
622C2×Q8—32no—
623C2×Q8—32no—
624C2×Q8—34no—
625C2×Q8—64no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8—64no—
630C2×Q8—64no—
631C2×Q8—242no—
632C2×Q8—244no—
633C2×Q8C23×D311yescharacteristic
634C2×Q8C23×D311yescharacteristic
635C2×D4—21no—
636C2×D4—21no—
637C2×D4C23×D311yescharacteristic
638C2×D4C23×D311yescharacteristic
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—64no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4D3×D411yescharacteristic
649C22×C4D3×D411yescharacteristic
650C22×C4C23×D311yescharacteristic
651Q16—22no—
652Q16—68no—
653SD16—22no—
654SD16—22no—
655SD16—68no—
656D8—22no—
657M16—64no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—34no—
661C2×C8C23×D311yescharacteristic
662C2×C8C23×D311yescharacteristic
663C2×C8C23×D311yescharacteristic
664C2×C8C23×D311yescharacteristic
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—32no—
670C4⋊C4—32no—
671C4⋊C4—32no—
672C4⋊C4—32no—
673C4⋊C4—34no—
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—64no—
677C4⋊C4—64no—
678C4⋊C4—64no—
679C4⋊C4—64no—
680C4⋊C4—64no—
681C4⋊C4—64no—
682C4⋊C4—64no—
683C4⋊C4—64no—
684C4⋊C4—62no—
685C4⋊C4—62no—
686C4⋊C4—62no—
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—62no—
691C4⋊C4C23×D311yescharacteristic
692C4⋊C4C23×D311yescharacteristic
693C4⋊C4C23×D311yescharacteristic
694C4⋊C4C23×D311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—34no—
702C22⋊C4—64no—
703C22⋊C4—64no—
704C22⋊C4—64no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—34no—
712C42—64no—
713C42—64no—
714C42—64no—
715C42D3×D411yescharacteristic
716C42D3×D411yescharacteristic
717C42C23×D311yescharacteristic
718C42C23×D311yescharacteristic
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3#54812yes—
728C22×C3C23×D411yescharacteristic
729C3×C4—22no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4#54812yes—
738C3×C4#57712yes—
739C3×C4#57812yes—
740C3×C4C22×#4111yescharacteristic
741C3×C4C2×2−1+411yescharacteristic
742Dic3—24no—
743Dic3—24no—
744Dic3—44no—
745Dic3—44no—
746C23—21no—
747C23—21no—
748C23C2×D3×D411yescharacteristic
749Q8—21no—
750Q8—21no—
751Q8—21no—
752Q8—64no—
753Q8—64no—
754Q8—64no—
755Q8—64no—
756Q8—124no—
757Q8—124no—
758Q8—242no—
759Q8—244no—
760Q8C2×#23512yes—
761D4—24no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—42no—
766D4C2×#23512yes—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—64no—
784C2×C4—64no—
785C2×C4—124no—
786C2×C4—244no—
787C2×C4—242no—
788C2×C4C2×#23512yes—
789C2×C4C2×D3×D411yescharacteristic
790C2×C4C2×D3×D411yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4C2×D3×D411yescharacteristic
794C2×C4#101012yes—
795C2×C4C24×D311yescharacteristic
796C8—21no—
797C8—21no—
798C8—21no—
799C8—21no—
800C8—64no—
801C2×C3—22no—
802C2×C3—42no—
803C2×C3—81no—
804C2×C3C2×#54811yescharacteristic
805C2×C3C2×#57711yescharacteristic
806C2×C3C2×#57811yescharacteristic
807C22—21no—
808C22—21no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22#555212yes—
816C22C22×D3×D411yescharacteristic
817C4—21no—
818C4—21no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—64no—
826C4—64no—
827C4—124no—
828C4—124no—
829C4#555212yes—
830C4#577012yes—
831C4#577112yes—
832C4C22×#23511yescharacteristic
833C4C2×#101011yescharacteristic
834C3#6133011yescharacteristic, complemented, Sylow
835C2—22no—
836C2—42no—
837C2—81no—
838C2C2×#555211yescharacteristic
839C2C2×#577011yescharacteristic
840C2C2×#577111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×#135C2
socleC22×C3C23×D4
prime radicalC2×C3×#135C22
hypercenterC4×#135D3
hypocenterC3#61330
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #85830C2semidirect
2. #85828C2semidirect
5. #82533C2semidirect
6. #82508C2semidirect
7. #79702C2semidirect
8. #79699C2semidirect
9. #79628C2semidirect
10. #79626C2semidirect
11. #79623C2semidirect
12. #79619C2semidirect
13. #79571C2semidirect
14. #79568C2semidirect
15. #79198C2semidirect
16. #78828C2semidirect
17. #78821C2semidirect
18. C2×#4681C2semidirect
19. #78445C2semidirect
834. C3#61330semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#858302
#858282
C3×C4×#1352
#839022
#825332
#825082
#797022
#796992
#796282
#796262
#796232
#796192
#795712
#795682
#791982
#788282
#788212
C2×#46812
#784452
#613303